The Difference Between Dice and Dice Loss

When doing image segmentation using CNNs, we often hear about the Dice coefficient, and sometimes we see the term dice loss. A lot of us get confused between these two metrics.

Dice coefficient and Dice loss are closely related, but they are not the same thing. Dice coefficient is an evaluation metric that measures overlap between a predicted mask and the ground truth mask. Dice loss is a training objective derived from that metric, commonly defined as 1 – Dice coefficient.

Before talking about Dice loss, let’s first define the Dice coefficient. Once that is clear, Dice loss becomes easier to understand because it is usually a simple transformation of the Dice coefficient.

Dice coefficient

When we do semantic segmentation, we often evaluate the model during validation or testing by comparing the predicted mask with the ground truth mask. The Dice coefficient is one of the most common overlap metrics for this. For binary segmentation, it is two times the intersection between the ground truth and the predicted mask, divided by the sum of the ground truth mask and the predicted mask.

In validation or testing, Dice is usually calculated on binary or thresholded masks. During training, Dice loss is usually calculated on soft probability maps so that the loss remains differentiable and can be used for backpropagation.

Let’s make this clearer:

Circle A represents the predicted mask, and circle B represents the ground truth.

The yellow area is the intersection between the ground truth and the predicted mask.

This is the Dice coefficient: as the intersection increases, the Dice value increases as well.

The minimum value that Dice can take is 0, which happens when there is no overlap between the predicted mask and the ground truth mask, assuming at least one of the masks contains foreground pixels. If both masks are empty, the denominator becomes zero, so implementations usually add a small smoothing term or define the empty-empty case separately.

The maximum value that Dice can take is 1, which means perfect overlap between the predicted mask and the ground truth mask for the evaluated class. In that case, the intersection is equal to both A and B because the prediction and the ground truth are the same. When multiplying the intersection by 2, we get 2 times the same value divided by 2 times the same value, so the result is 1. Let me show you this in a graph.

The key point is that the Dice coefficient has a value between 0 and 1. Values closer to 1 mean better overlap between the prediction and the ground truth.

The dice loss

Now that the Dice coefficient is clear, Dice loss is easy to understand too. The best Dice values are close to 1, while loss values should become smaller as the model improves because they are used to update weights during backpropagation.

So we can transform the Dice coefficient into a loss value with a simple equation:

By looking at this equation, we can conclude that when the Dice value goes up, the Dice loss goes down. When Dice reaches its maximum value of 1, Dice loss becomes 0. This means perfect overlap for that batch, mask, or class under the chosen implementation, but it does not prove that the model is perfect in every situation.